There are several weapons I've found to be effective. My favorites include the Dragon Bone Smasher, Mirdan Hammer, War Scythe, Uchigatana, Great Sword, Great Axe, Meat Cleaver, and Blueblood Sword. If you figure out an attack stat you like best, I can help recommend weapons and upgrade paths. Each attack stat tends to have a few special weapons, such as the Dragon Bone Smasher boosted by STR. I use either a Mirdan Hammer or War Scythe with every build. I always carry one of those. The upgrade path you need from Ed and the ores you must collect depends on your stats. If you look on the first page of this thread, you see some examples of builds I use and weapons associated with them.
I think the Dragon Bone Smasher is probably out of the question now. I have finished all of world 2 but didn't get PWWT (but looking at my WT map I think I am very close) and there doesn't seem to be an easy way to raise my WT (or WT in general which I think is a bit of a flaw with the game) so I think I won't be getting it. I have found its easy to lower your WT but hard to raise it.
It's only useful for specialized STR builds, but it's among the best weapons in the game for those that are set up to use it. 1-hit knockdown, huge damage, significant fire damage resistance, and it can be buffed. An easier to acquire weapon that should work with almost any build is the Mirdan Hammer. It's a random drop from miners near the beginning of 2-2. Right side, tunnel above the pit. Easy to get and downright beastly when you learn how to 2-hand it. The similar War Sythe is probably the most underrated weapon in the game. It can't break guards as well as the Hammer, but it causes bleeding and is almost as deadly. I love surprising people with it. The Uchigatana is also deadly, but it's a bit fragile. Like 70 durability I think. You can really tear enemies up with it, though. I always carry a pole arm weapon as an alternate in case the Uchi breaks, which is only occasionally.
I levelled it up a little yesterday with some sharp stones to +2 but it was seriously weak compared to my Dragon Long Sword. I imagine it gets better as my stats do and when I really start to put some stones and souls into it. I did a little farming last night for dragon stone chunks and managed to get enough to get my Dragon Long Sword to +4. Having trouble now farming the remaining chunks for +5 but I have the shards and pure stone so hopefully they will turn up. Shame those black phantoms near the entrance to the crystal lizard cave don't respawn as one of them dropped 3.
You're going to get the power from the next branch of upgrades AFTER Sharpstones. For example, with these stats, here's roughly the damange you'd do with a Magic boosted Moon or Crescent Uchi: STR 22 DEX 16 MAG 40 Moon Uchigatana +5 395 Crescent Uchigatana +5 380 (+1 Mana Regen / 3 seconds) My guess is that these Uchigatanas are going to outdamage your Dragon Long Sword, and the further you improve your attack stat, the bigger the disparity will be. Make sure you're doing your upgrades of those types of weapons with Ed, as additional upgrade paths will open up with him. I think the guy in the Nexus will mostly do Hardstones, Sharpstones, and I think Clearstones. Ed will let you upgrade with every type of ore.